Answer:
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It contains the analysis of your query and should assist you in visualizing it.
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Hello!
(x+a)·(x+b) equals x²+xa+xb+ab which simplifies to x²-12x-45
x² equals x²
xa+xb can be expressed as (a+b)x = -12x thus, (a+b) = -12
ab equals -45
Under what conditions do (a+b) equal -12 and ab equal -45?
+3-15 results in -12 while (+3)(-15) gives -45
-3-15 yields -18 and (-3)(-15) results in +45
+3+15 produces +18 and (+3)(+15) also equal to +45
-3+15 equals +12 and (-3+15) results in -45
Conclusion:
(x+3)(x-15)
Answer:
The sequence decreases by 5
thus the subsequent numbers are
-13,-18,-23,-28
THE FUNCTION IS CONTINUOUS - True
The table indicates that for every hour indicated, there is a corresponding amount of juice (cups) provided. The graph would represent a linear progression between the hours of 4 and 8 without any discontinuities.
TIME IS THE DEPENDENT VARIABLE - False
Time acts as the independent variable since it remains unaffected by any other factors. Conversely, the number of cups is contingent upon the hours, categorizing it as a dependent variable.
THE SCENARIO IS CHARACTERIZED BY
A LINEAR FUNCTION AS THE RATE OF CHANGE IS CONSTANT - True
The rate of change is a steady 53 cups per hour, indicating a linear function.
AS TIME INCREASES, THERE ARE FEWER CUPS OF JUICE POURED EACH HOUR - False
Since the rate of change is positive, the cups poured each hour will actually increase.
FOR EACH EXTRA HOUR, 53 CUPS OF JUICE ARE POURED - True
The hourly difference in cups poured is consistently 53.
